FASTLens (FAst STatistics for weak Lensing) : Fast method for Weak Lensing Statistics and map making

With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever greater precision. However this increased accuracy also places greater demands on the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two point-statistics of the cosmic shear field. These can either be studied directly using the two-point correlation function, or in Fourier space, using the power spectrum. But analyzing weak lensing data inevitably involves the masking out of regions or example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only $N \log N$ operations, leading to a new image from which we can compute straight forwardly and with a very good accuracy both the pow er spectrum and the bispectrum. We propose then a new method to compute the bispectrum with a polar FFT algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally we propose a new method for dark matter mass map reconstruction from shear observations which integrates this new inpainting concept. A range of examples based on 3D N-body simulations illustrates the results.Comment: Final version accepted by MNRAS. The FASTLens software is available from the following link : http://irfu.cea.fr/Ast/fastlens.software.ph

Cosmological models discrimination with Weak Lensing

Weak gravitational lensing provides a unique method to map directly the dark matter in the Universe. The majority of lensing analyses uses the two-point statistics of the cosmic shear field to constrain the cosmological model yielding degeneracies, such as that between sigma_8 and Omega_M respectively the r.m.s. of the mass fluctuations at a scale of 8 Mpc/h and the matter density parameter both at z = 0. However, the two-point statistics only measure the Gaussian properties of the field and the weak lensing field is non-Gaussian. It has been shown that the estimation of non-Gaussian statistics on weak lensing data can improve the constraints on cosmological parameters. In this paper, we systematically compare a wide range of non-Gaussian estimators in order to determine which one provides tighter constraints on the cosmological parameters. These statistical methods include skewness, kurtosis and the Higher Criticism test in several sparse representations such as wavelet and curvelet; as well as the bispectrum, peak counting and a new introduced statistic called Wavelet Peak Counting (WPC). Comparisons based on sparse representations show that the wavelet transform is the most sensitive to non-Gaussian cosmological structures. It appears also that the best statistic for non-Gaussian characterization in weak lensing mass maps is the WPC. Finally, we show that the sigma_8 -Omega_m degeneracy could be even better broken if the WPC estimation is performed on weak lensing mass maps filtered by the wavelet method, MRLens.Comment: Submitted to A&

A Catalog of Diffuse X-ray-Emitting Features within 20 pc of Sgr A*: Twenty Pulsar Wind Nebulae?

We present a catalog of 34 diffuse features identified in X-ray images of the Galactic center taken with the Chandra X-ray Observatory. Several of the features have been discussed in the literature previously, including 7 that are associated with a complex of molecular clouds that exhibits fluorescent line emission, 4 that are superimposed on the supernova remnant Sgr A East, 2 that are coincident with radio features that are thought to be the shell of another supernova remnant, and one that is thought to be a pulsar wind nebula only a few arcseconds in projection from Sgr A*. However, this leaves 20 features that have not been reported previously. Based on the weakness of iron emission in their spectra, we propose that most of them are non-thermal. One long, narrow feature points toward Sgr A*, and so we propose that this feature is a jet of synchrotron-emitting particles ejected from the supermassive black hole. For the others, we show that their sizes (0.1-2 pc in length for D=8 kpc), X-ray luminosities (between 10^32 and 10^34 erg/s, 2-8 keV), and spectra (power laws with Gamma=1-3) are consistent with those of pulsar wind nebulae. Based on the star formation rate at the Galactic center, we expect that ~20 pulsars have formed in the last 300 kyr, and could be producing pulsar wind nebulae. Only one of the 19 candidate pulsar wind nebulae is securely detected in an archival radio image of the Galactic center; the remainder have upper limits corresponding to L_R<la10^31 erg/s. These radio limits do not strongly constrain their natures, which underscores the need for further multi- wavelength studies of this unprecedented sample of Galactic X-ray emitting structures.Comment: 14 pages, 8 figures, 5 in color. Submitted to Ap

Curvelet analysis of asteroseismic data I: Method description and application to simulated sun-like stars

Context: The detection and identification of oscillation modes (in terms of their $\ell$, $m$ and successive $n$) is a great challenge for present and future asteroseismic space missions. The "peak tagging" is an important step in the analysis of these data to provide estimations of stellar oscillation mode parameters, i.e., frequencies, rotation rates, and further studies on the stellar structure. Aims: To increase the signal-to-noise ratio of the asteroseismic spectra computed from time series representative of MOST and CoRoT observations (30- and 150-day observations). Methods: We apply the curvelet transform -- a recent image processing technique which looks for curved patterns -- to echelle diagrams built using asteroseismic power spectra. In this diagram the eigenfrequencies appear as smooth continuous ridges. To test the method we use Monte Carlo simulations of several sun-like stars with different combinations of rotation rates, rotation-axis inclination and signal-to-noise ratios. Results: The filtered diagrams enhance the contrast between the ridges of the modes and the background allowing a better tagging of the modes and a better extraction of some stellar parameters. Monte Carlo simulations have also shown that the region where modes can be detected is enlarged at lower and higher frequencies compared to the raw spectra. Even more, the extraction of the mean rotational splitting from modes at low frequency can be done more easily than using the raw spectrum.Comment: 8 pages, 6 figures, accepted for publication in A&

Full-Sky Weak Lensing Simulation with 70 Billion Particles

We have performed a 70 billion dark-matter particles N-body simulation in a 2 $h^{-1}$ Gpc periodic box, using the concordance, cosmological model as favored by the latest WMAP3 results. We have computed a full-sky convergence map with a resolution of $\Delta \theta \simeq 0.74$ arcmin$^{2}$, spanning 4 orders of magnitude in angular dynamical range. Using various high-order statistics on a realistic cut sky, we have characterized the transition from the linear to the nonlinear regime at $\ell \simeq 1000$ and shown that realistic galactic masking affects high-order moments only below $\ell < 200$. Each domain (Gaussian and non-Gaussian) spans 2 decades in angular scale. This map is therefore an ideal tool for testing map-making algorithms on the sphere. As a first step in addressing the full map reconstruction problem, we have benchmarked in this paper two denoising methods: 1) Wiener filtering applied to the Spherical Harmonics decomposition of the map and 2) a new method, called MRLens, based on the modification of the Maximum Entropy Method on a Wavelet decomposition. While the latter is optimal on large spatial scales, where the signal is Gaussian, MRLens outperforms the Wiener method on small spatial scales, where the signal is highly non-Gaussian. The simulated full-sky convergence map is freely available to the community to help the development of new map-making algorithms dedicated to the next generation of weak-lensing surveys.Comment: 7 pages, 6 figures, accepted in Astronomy and Astrophysics, final version after language editin

The Cosparse Analysis Model and Algorithms

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments.Comment: Submitted (2011

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $\ell_1$-constraints, using a gradient method, with projection on $\ell_1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page

The application of a Trous wave filtering and Monte Carlo analysis on SECIS 2001 solar eclipse observations

8000 images of the Solar corona were captured during the June 2001 total Solar eclipse. New software for the alignment of the images and an automated technique for detecting intensity oscillations using multi scale wavelet analysis were developed. Large areas of the images covered by the Moon and the upper corona were scanned for oscillations and the statistical properties of the atmospheric effects were determined. The a Trous wavelet transform was used for noise reduction and Monte Carlo analysis as a significance test of the detections. The effectiveness of those techniques is discussed in detail.Comment: 17 pages, 8 figures, accepted by Solar Physics Journal for publication in Topical Issue: "Frontiers in Solar Image Processing

Do maternal environmental conditions during reproductive development induce genotypic selection in Picea abies?

In forest trees, environmental conditions during reproduction can greatly influence progeny performance. This phenomenon probably results from adaptive phenotypic plasticity but also may be associated with genotypic selection. In order to determine whether selective effects during the reproduction are environment specific, single pair-crosses of Norway spruce were studied in two contrasted maternal environments (warm and cold conditions). One family expressed large and the other small phenotypic differences between these crossing environments. The inheritance of genetic polymorphism was analysed at the seed stage. Four parental genetic maps covering 66 to 78% of the genome were constructed using 190 to 200 loci. After correcting for multiple testing, there is no evidence of locus under strong and repeatable selection. The maternal environment could thus only induce limited genotypic-selection effects during reproductive steps, and performance of progenies may be mainly affected by a long-lasting epigenetic memory regulated by temperature and photoperiod prevailing during seed production.L'environnement maternel induit-il une sélection génotypique durant les différents stades de reproduction chez Picea abies ?. Chez les arbres forestiers, les conditions environnementales durant la reproduction peuvent influencer les performances des descendants. Ce phénomène reflète probablement la plasticité phénotypique, mais également il pourrait être associé à une sélection génotypique. Afin de déterminer si des effets sélectifs durant la reproduction sont spécifiques d'un environnement donné, deux familles d'épicéa commun non apparentées ont été obtenues par croisements dirigés dans deux environnements maternels contrastés (conditions chaude et froide). La première famille exprimait de larges différences phénotypiques entre les deux environnements tandis que la seconde ne montrait pas de différence significative. La transmission des polymorphismes génétiques a été étudiée au stade de la graine. Quatre cartes génétiques parentales couvrant 66 à 78 % du génome ont été construites. Aucun effet de sélection n'a été mis en évidence aux différents locus étudiés. L'environnement maternel n'induirait donc que des effets de sélection génotypique relativement faibles durant les stades de la reproduction. Les performances des descendants seraient principalement affectées par une mémoire épigénétique durable régulée par la température et la photopériode régnant durant la production des graines